Remark 1.1 The above proof of the abstract Birman-Schwinger principle is due to Birman-Solomyak [1]}. It is much simpler than various other known proofs of the Birman-Schwinger principle, even in the case of Schrödinger operators on \(\mathbb {R}^n\) . In fact, we have merely recasted the proof of [1]} into the framework of [3]}.

